Transition threshold for the 3D Couette flow in Sobolev space

Abstract

In this paper, we study the transition threshold of the 3D Couette flow in Sobolev space at high Reynolds number $\text{Re}$. It was proved that if the initial velocity $v_0$ satisfies $\Vert v_0-(y,0,0){\Vert }_{H^2}\le c_0{\text{Re}}^{-1}$, then the solution of the 3D Navier-Stokes equations is global in time and does not transition away from the Couette flow. This result confirms the transition threshold conjecture in physical literatures.

arXiv comment49 pages

References in corpus (3)

• Metastability of Kolmogorov flows and inviscid damping of shear flows
• Linear inviscid damping and vorticity depletion for shear flows
• Stability of the Couette flow at high Reynolds number in 2D and 3D

Cited by in corpus (15)

• Transition threshold for the 3D Couette flow in a finite channel
• Inviscid damping near the Couette flow in a channel
• Diffusion and mixing in fluid flow via the resolvent estimate
• Enhanced dissipation in the Navier-Stokes equations near the Poiseuille flow
• Stability threshold of the 2D Couette flow in Sobolev spaces
• Nonlinear inviscid damping near monotonic shear flows
• The linearized Vlasov and Vlasov-Fokker-Planck equations in a uniform magnetic field
• Stability threshold for 2D shear flows of the Boussinesq system near Couette
• Inviscid damping and enhanced dissipation of the boundary layer for 2D Navier-Stokes linearized around Couette flow in a channel
• Enhanced dissipation for the 2D Couette flow in critical space
• Separation of time-scales in drift-diffusion equations on ${\mathbb{R}}^2$
• Stable mixing estimates in the infinite Péclet number limit
• Uniqueness and uniform structural stability of Poiseuille flows in a periodic pipe with Navier boundary conditions
• On the Sobolev stability threshold of 3D Couette flow in a homogeneous magnetic field
• Instability of the Kolmogorov flow in a wall-bounded domain